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Fatima claims she can prove the two triangles shown are congruent using the SAS (Side-Angle-Side)

theorem.

1. Is she correct? Yes or No.
2. Explain why.

Fatima claims she can prove the two triangles shown are congruent using the SAS (Side-example-1

1 Answer

6 votes

Explanation:

1. no

2.

SAS congruence theorem: if two sides and the angle between these two sides are congruent (equally sized) to the corresponding sides and angle of another triangle, then the two triangles are congruent.

in our case the equal angle is not between the 2 known sides. therefore, SAS cannot be used to prove congruence.

FYI :

SSA (side-side-angle) can be used here.

that means 2 sides and one (not between the 2 sides) angle are equally sized (congruent).

if the given angle would be acute (less than 90°), and the 2 given sides have different lengths, then this would not apply, as we could create 2 different triangles that are not congruent (by "swinging" the shorter known side and cross it with the line of the third, unknown side we get 2 different intersection points and therefore triangles).

but :

if the given angle is right or obtuse (greater than 90°), only one triangle can be produced, in which case SSA is a legitimate congruence theorem.

and that is the case here. the given angle is clearly obtuse.

therefore, by using SSA we can prove congruence.

just not SAS.

User Matt Dressel
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